Journal
PHYSICAL REVIEW LETTERS
Volume 129, Issue 24, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.129.246402
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Funding
- Ambizione Grant by the Swiss National Science Foundation [185806]
- University of Alberta startup fund UOFAB Startup Boettcher
- Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grants [RGPIN-2021-02534, DGECR2021-00043]
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [258499086-SFB 1170]
- Wurzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter-ct.qmat Project [39085490-EXC 2147]
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programm [ERC-StG-Neupert-757867-PARATOP]
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In this study, elementary models of hyperbolic topological band insulators were introduced, and their nontrivial topology was revealed by computing topological invariants. The bulk-boundary correspondence was demonstrated, and the robustness of these models against disorder was confirmed.
Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band structure in a four-(or higher-) dimensional momentum space. To explore the uncharted topological aspects arising in hyperbolic band theory, we here introduce elementary models of hyperbolic topological band insulators: the hyperbolic Haldane model and the hyperbolic Kane-Mele model; both obtained by replacing the hexagonal cells of their Euclidean counterparts by octagons. Their nontrivial topology is revealed by computing topological invariants in both position and momentum space. The bulk-boundary correspondence is evidenced by comparing bulk and boundary density of states, by modeling propagation of edge excitations, and by their robustness against disorder.
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